Chemistry - Ionic Equilibrium Question with Solution | TestHub

pH = 8.5: $\left[{\mathrm{H}}^{+}\right]=3.16\times 10^{-9}\mathrm{M}$ and $\left[{\mathrm{OH}}^{-}\right]=3.16\times 10^{-6}\mathrm{M}$.

Hydrolysis of ${\mathrm{X}}^{-}$ gives equal $\mathrm{HX}$ and ${\mathrm{OH}}^{-}$: $\mathrm{HX}=3.16\times 10^{-6}\mathrm{M}$.

$\left[{\mathrm{X}}^{-}\right]=\frac{K_a\mathrm{HX}}{\left[{\mathrm{H}}^{+}\right]}=\frac{2.0\times 10^{-5}\times 3.16\times 10^{-6}}{3.16\times 10^{-9}}=0.020\mathrm{M}$.

$\left[{\mathrm{Ag}}^{+}\right]=\left[{\mathrm{X}}^{-}\right]+\mathrm{HX}=0.020\mathrm{M}$ (the $\mathrm{HX}$ part is negligible).

$K_{sp}=0.020\times 0.020=4.0\times 10^{-4}$.

Answer: (C).